Simplify to lowest terms. $\dfrac{84}{48}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 84 and 48? $84 = 2\cdot2\cdot3\cdot7$ $48 = 2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(84, 48) = 2\cdot2\cdot3 = 12$ $\dfrac{84}{48} = \dfrac{7 \cdot 12}{ 4\cdot 12}$ $\hphantom{\dfrac{84}{48}} = \dfrac{7}{4} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{84}{48}} = \dfrac{7}{4} \cdot 1$ $\hphantom{\dfrac{84}{48}} = \dfrac{7}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{84}{48}= \dfrac{2\cdot42}{2\cdot24}= \dfrac{2\cdot 2\cdot21}{2\cdot 2\cdot12}= \dfrac{2\cdot 2\cdot 3\cdot7}{2\cdot 2\cdot 3\cdot4}= \dfrac{7}{4}$